Calculating the percentage by mass of methane in the gas mixture:

To calculate the percentage by mass of methane in the gas mixture, we need to know the molar mass of each gas in the mixture.

- The molar mass of helium (He) is 4.00 g/mol
- The molar mass of methane (CH4) is 16.04 g/mol (12.01 g/mol for carbon + 4 x 1.01 g/mol for hydrogen)

Step 1: Calculate the total molar mass of the gas mixture

To calculate the total molar mass of the gas mixture, we need to take into account the percentage of each gas in the mixture:

- 25% He = 0.25 mol He
- 75% CH4 = 0.75 mol CH4

We can now calculate the total molar mass of the gas mixture as follows:

Total molar mass = (0.25 mol He x 4.00 g/mol) + (0.75 mol CH4 x 16.04 g/mol)
Total molar mass = 12.01 g/mol

Step 2: Calculate the mass of methane in the mixture

To calculate the mass of methane in the mixture, we need to know the mass fraction of methane in the mixture:

Mass fraction of methane = (mol fraction of methane x molar mass of methane) / total molar mass

- Mol fraction of methane = 0.75
- Molar mass of methane = 16.04 g/mol
- Total molar mass = 12.01 g/mol

Mass fraction of methane = (0.75 x 16.04 g/mol) / 12.01 g/mol
Mass fraction of methane = 1.00

This means that the mass fraction of methane in the mixture is 100%, so the percentage by mass of methane in the mixture is approximately 100%.